What question did this study set out to answer?

The research aims to solve the planar Skorokhod embedding problem specifically for cases where p=1, which had previously been left unresolved.

A Note on the Planar Skorokhod Embedding Problem

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This note demonstrates a solution for the planar Skorokhod embedding problem for cases with p=1, suggesting a closure of previous investigations.

The research aims to solve the planar Skorokhod embedding problem specifically for cases where p=1, which had previously been left unresolved.
Analyzed properties of probability distributions with finite moments
Utilized the Hilbert transform of the quantile function
Developed a solution framework for planar Brownian motion
Established solvability of the planar Skorokhod embedding for p=1
Identified conditions related to the integrability of the Hilbert transform
Closed the gap in existing literature regarding embeddings for p=1

Maher Boudabra (2026) studied this question.

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This note demonstrates a solution for the planar Skorokhod embedding problem for cases with p=1, suggesting a closure of previous investigations.